**Multiplying decimals by powers of 10 :**

It is observed that

3.7 = 37/10

3.72 = 372/10²³

0

3.723 = 3723/10³

Thus, it is found that depending on the position of the decimal point the decimal number can be converted to a fraction with denominator 10 , 10² or 10³.

Now let us see what would happen if a decimal number is multiplied by 10 or 10² or 10³.

For example,

**3.23** x 10 = **32.3**

In the above multiplication, since 10 has the power 1, decimal point shifted to the right by one place.

**3.23** x 10² = **323**

In the above multiplication, since 10² has the power 2, decimal point shifted to the right by two places.

**3.23** x 10³ = **3230**

In the above multiplication, since 10³ has the power 3, decimal point shifted to the right by three places.

**Problem 1 :**

Multiply 3.723 by 10

**Solution :**

We multiply by 3.723 by 10. So, we have to move the decimal point one digit to the right.

3.723 x 10 = 37.23

Multiplying 3.723 by 10, we get 37.23

**Problem 2 :**

Multiply 3.723 by 100

**Solution :**

We multiply by 3.723 by 100. So, we have to move the decimal point two digits to the right.

3.723 x 100 = 372.3

Multiplying 3.723 by 100, we get 372.3

**Problem 3 :**

Multiply 3.723 by 1000

**Solution :**

We multiply by 3.723 by 1000. So, we have to move the decimal point two digits to the right.

3.723 x 1000 = 3723

Multiplying 3.723 by 1000, we get 3723

**Problem 4 :**

The price of a fruit is $3.52 per lb. Find the cost of 10 lbs of fruits.

**Solution :**

Given : Cost of 1 lb of fruit = $3.52

Then, the cost of 10 lbs of fruits is

= 10 x 3.52

We multiply by 3.52 by 10. So, we have to move the decimal point one digit to the right.

So, we get

= 35.2

Hence, the cost of 10 lbs of fruits is $35.2

**Problem 5 :**

A person walks regularly in the morning. If the speed of his walking is 43.26 ft per minute, Find the distance covered by him in 100 minutes.

**Solution :**

Given : Speed is 43.26 ft per minute.

So, distance covered in one minute is 43.26 ft.

We all know the formula for distance.

That is,

Distance = Speed x Time

To know the distance covered in 100 minutes, we have to plug time = 100 and the speed is 43.26

Distance = 43.26 x 100

We multiply by 43.26 by 100. So, we have to move the decimal point two digits to the right.

So, we get

Distance = 4326 ft

Hence, the distance covered by him in 100 minutes is 4326 ft.

**Problem 6 :**

One-thousandth of a certain number is 0.003. What is the number?

**Solution :**

Given : One-thousandth of a certain number is 0.003

Let "a" be the number.

Then, from the given information, we get

(1/1000) x a = 0.003

Multiplying by 1000 on both sides, we get

a = 0.003 x 1000

We multiply by 0.003 by 1000. So, we have to move the decimal point three digits to the right.

So, we get

a = 3

Hence, the the number is 3.

After having gone through the stuff given above, we hope that the students would have understood "Multiplying decimals by powers of 10".

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